Arsenal have been drawn in the same group as BATE Borisov, Cologne and Red Star Belgrade in the Europa League.
It is the first time in 20 years that the Gunners, who finished fifth in the Premier League last season, have started a season in Europe’s second-tier competition.
Everton are in the same group as Lyon, who host the final on 16 May 2018.
The Toffees will also face Italian Serie A side Atalanta and Apollon Limassol of Cyprus.
Everton, who completed their play-off victory over Croatian side Hajduk Split on Thursday, are in Europe for the first time since 2014-15.
The 48-team draw for this season’s competition included Sweden’s Ostersund, managed by Englishman Graham Potter, the former Stoke City and West Brom full-back.
Ostersund will play Spain’s Athletic Bilbao, Germany’s Hertha Berlin and Zorya Luhansk of Ukraine.
The group stage begins on 14 September.